Markov chain Monte Carlo estimation of default and recovery: dependent via the latent systematic factor

TL;DR

This paper presents a Bayesian MCMC approach for estimating a dependent loss given default and recovery model using latent systematic risk factors, effectively quantifying uncertainties with small datasets.

Contribution

It introduces a Bayesian inference methodology with MCMC for joint estimation of model parameters and latent factors in default and recovery models, handling small datasets effectively.

Findings

Bayesian approach outperforms maximum likelihood in small samples.

Model captures dependence between defaults and recoveries via latent factors.

Method is extendable to complex portfolios and multiple factors.

Abstract

It is a well known fact that recovery rates tend to go down when the number of defaults goes up in economic downturns. We demonstrate how the loss given default model with the default and recovery dependent via the latent systematic risk factor can be estimated using Bayesian inference methodology and Markov chain Monte Carlo method. This approach is very convenient for joint estimation of all model parameters and latent systematic factors. Moreover, all relevant uncertainties are easily quantified. Typically available data are annual averages of defaults and recoveries and thus the datasets are small and parameter uncertainty is significant. In this case Bayesian approach is superior to the maximum likelihood method that relies on a large sample limit Gaussian approximation for the parameter uncertainty. As an example, we consider a homogeneous portfolio with one latent factor. However, the approach can be easily extended to deal with non-homogenous portfolios and several latent factors.